Welcome to FT!
As the previous poster said, recommendations may vary greatly. Assuming you want to minimize out-of-pocket ticket expenses and maximize mileage earning potential, I would suggest the following:
- If your credit will bear it, open Citi AA credit cards which give you 50K points each + $150 statement credit. Each of you can get 2 cards, giving you 4 r/t tickets each.
- If that's not an option and you have to buy the tickets:
- If earning status is more important, stick with one airline, as 5 economy r/t tickets should give you low-tier status
- If you plan to redeem for short-haul flights, consider the British Airways FF program, as it has favorable redemption rates (including its partner, American Airlines) and allows you to pool mileage with your fiance.
Hopefully this will help get you started. Others will surely chime in as well.